TY - JOUR

T1 - Libraries, tools, and interactive systems for verified computations four case studies

AU - Baker Kearfott, R.

AU - Neher, Markus

AU - Oishi, Shin'ichi

AU - Rico, Fabien

PY - 2004/12/1

Y1 - 2004/12/1

N2 - As interval analysis-based reliable computations find wider application, more software is becoming available. Simultaneously, the applications for which this software is designed are becoming more diverse. Because of this, the software itself takes diverse forms, ranging from libraries for application development to fully interactive systems. The target applications range from fairly general to specialized. Here, we describe the design of four freely available software systems providing validated computations. Oishi provides Slab, a complete, high-performance system for validated linear algebra whose user interface mimics both Matlab's M-files and a large subset of Matlab's commandline functions. In contrast, CADNA (Fabien Rico) is a C++ library designed to give developers of embedded systems access to validated numeric computations. Addressing global constrained optimization and validated solution of nonlinear algebraic systems, Kearfott's GlobSol focuses on providing the most practical such system possible without specifying non-general problem structure; Kearfott's system has a Fortran-90 interface. Finally, Neher provides a mathematically sound stand-alone package ACETAF with an intuitive graphical user interface for computing complex Taylor coefficients and their bounds, radii of convergence, etc. Overviews of each package's capabilities, use, and instructions for obtaining and installing appear.

AB - As interval analysis-based reliable computations find wider application, more software is becoming available. Simultaneously, the applications for which this software is designed are becoming more diverse. Because of this, the software itself takes diverse forms, ranging from libraries for application development to fully interactive systems. The target applications range from fairly general to specialized. Here, we describe the design of four freely available software systems providing validated computations. Oishi provides Slab, a complete, high-performance system for validated linear algebra whose user interface mimics both Matlab's M-files and a large subset of Matlab's commandline functions. In contrast, CADNA (Fabien Rico) is a C++ library designed to give developers of embedded systems access to validated numeric computations. Addressing global constrained optimization and validated solution of nonlinear algebraic systems, Kearfott's GlobSol focuses on providing the most practical such system possible without specifying non-general problem structure; Kearfott's system has a Fortran-90 interface. Finally, Neher provides a mathematically sound stand-alone package ACETAF with an intuitive graphical user interface for computing complex Taylor coefficients and their bounds, radii of convergence, etc. Overviews of each package's capabilities, use, and instructions for obtaining and installing appear.

KW - Embedded systems

KW - Global optimization

KW - Interactive software systems

KW - Interval arithmetic

KW - Numerical linear algebra

KW - Software libraries

KW - Stochastic arithmetic

KW - Taylor series

KW - Validated computations

UR - http://www.scopus.com/inward/record.url?scp=35048877236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35048877236&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:35048877236

VL - 2991

SP - 36

EP - 63

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -